The upstream transmissions on a digital cable system, e.g., transmission from a subscriber to a head-end such as a cable office, are typically done in the 5-65 MHz spectrum. Such transmissions may use symbol rates of, e.g., up to 2.5 MHz. For a fully digital implementation of an upstream modulator, RF Carrier samples are available at a frequency Fc which is above 2.times. RF.sub.max frequency. Hence for the mixing process to be done digitally, the base-band signal containing the information must also be available at an Fc sampling rate.
In many digital transmission systems the data symbol rate is programmable over a wide range (typically 64 Kbaud to 2.5 Mbaud). In such systems the modulator is frequently required to shape the symbol pulses, and interpolate them to the fc sample rate. Since a number of pulse shape specifications already exist in the industry, it is desirable for purposes of flexibility that both the Pulse Shaping Filter (Nyquist Filter) and/or the Interpolator filter used in a digital transmission system be programmable.
In various known modulators, the pulse shaping (Nyquist) filter and interpolator filter have been implemented as separate filters.
In modulators, the Nyquist filter must be designed so that it is capable of working at the highest symbol rate supported by the modulator. As the symbol rate increases, the complexity of multiplier hardware also increases. Thus, at the highest symbol rate, the Nyquist filter will require the most resources since it will use the most complex hardware implementations.
A programmable interpolator, intended to work with a modulator's programmable Nyquist filter, has to be designed so that it is capable of working at the slowest symbol rate. Interpolators generally require multiplier hardware resources proportional to the maximum interpolation ratio to be supported. The slower the input symbol rate, the greater the sampling rate translation that must be performed by the interpolator to translate the input waveform(sampled at input symbol rate) to an output waveform(sampled at a much higher sampling rate).
Thus, in contrast to the pulse shaping filter, the interpolator requires the most resources to implement when it is at the slowest symbol rate.
The conflicting requirements for hardware resources in terms of Nyquist and Interpolator filters leads to a sub-optimal implementation in terms of hardware efficiency when separate Nyquist and interpolator filters are used.
In order to improve implementation efficiency and thereby reduce the cost of digital modulators, there is a need for new and improved methods of implementing Nyquist and interpolator filters used in, e.g., digital modulators.